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We experimentally reveal the potential security risks for chaotic semiconductor lasers caused by time-delay signature (TDS). In order to eliminate TDS and enhance effective bandwidth, we propose a new scheme by introducing phase-modulation injection using Gaussian noise or pseudo-random binary sequence (PRBS) as phase-modulation signals. Our numerical results indicate that TDS elimination and bandwidth enhancement are obtained over a wide-parameter region of injection strength and frequency detuning. We further improve the scheme by usi